Just to make clear, this is not an AHC, I have that thought out, what I am wondering is what would be the results and what would be the external butterflies? Both empires would be less advanced, and I am not sure who would be superior although I am guessing Carthage.
Well, in 500 BC, the leader of the Dorian Greeks on Sicily would probably be Gela, as Syracuse was actually, compared to Gela, fairly weak at the time. It would take Gelo, the tyrant of Gela a decade after your date of 500 BC, to make Syracuse into the supreme Greek power in Sicily.
Now, I will bring up the Himera campaign as something to keep in mind in analyzing this POD, as that involved a (fairly) united Dorian Greek front, led by Syracuse, against (supposedly) about the largest Carthaginian invasion that Carthage would ever want to send. Gelo, the Gelan and, at that time, the Syracusan tyrant (he made Syracuse his base after conquering it), thwarted the Carthaginians at Himera in 480 BC, supposedly on the same day as either the Battle of Thermopylae, or Salamis. Whatever the case, it was a huge victory for the Greeks, that many people forget about.
As to your question, the Carthaginians were undoubtably stronger and more advanced then Syracuse at the time, and probably moreso then Gela, but that doesn't necessarily mean that they would be successful in a war, as Gelo proved by defeating a pretty strong Carthaginian attack. With a Greek victory, things probably turn out about the same as they did IOTL, with Carthage taking some time off in trying to take Sicily, and Syracuse (or, perhaps in this case, Gela?) growing in power with the absence of foreign intervention, and possibly a great victory as a feather in their cap. If Carthage were to win and conquer Sicily, the Malik in charge (likely Hamilcar, the Malik that fought and died at Himera) might gain enough power for the monarchy to keep that position stronger for longer (as Hamilcar's defeat did quite a bit to discredit the monarchy). You might also see Corinth, or Athens (probably Athens, but Corinth was the mother city for many of those colonies, including Syracuse), lead an expedition to help Greek rebels on Sicily, as part of their post-Xerxes activities, which could be quite interesting.